IndisputableMonolith.Foundation.LogicAsFunctionalEquation.AnalyticCounterexample
The AnalyticCounterexample module supplies the diagonal of an analytically reparameterized combiner in the local coordinate s where a equals s plus s squared. It builds on the quartic-log counterexample to produce a continuous symmetric combiner on the nonnegative reals. Researchers examining obstructions to the logic functional equation cite this construction when testing analytic reparameterizations. The module organizes its content through direct import of the quartic case and sibling definitions of reparametrized diagonals.
claimLet $C(x,y)= (log(x/y))^4$. The reparameterized diagonal is the function obtained by substituting the analytic change of variables with local coordinate $s$ satisfying $a=s+s^2$.
background
The module belongs to the LogicAsFunctionalEquation development and imports the quartic-log counterexample. That upstream result states that $C(x,y)=(log(x/y))^4$ defines a continuous symmetric combiner on the nonnegative range. The present module isolates the diagonal of the analytically reparameterized version of this combiner. The reparameterization uses the local coordinate $s$ defined by the quadratic relation $a=s+s^2$, which converts the original combiner into a form convenient for degree analysis.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the CountOnceComparison module, which requires that each constituent comparison is counted once and therefore demands a combiner affine in each variable separately (of the form $a + b u + c v + d u v$). It supplies the analytic reparameterized diagonal needed to test whether the quartic-log counterexample satisfies or obstructs that affine condition.
scope and limits
- Does not prove the full counterexample to the functional equation.
- Does not address discrete or integer-valued cases.
- Does not derive numerical bounds or physical constants.
- Does not connect to the phi-ladder or Recognition Science forcing chain.